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A286254 Compound filter: a(n) = P(A001511(n), A055396(1+n)), where P(n,k) is sequence A000027 used as a pairing function. 4
1, 5, 1, 13, 1, 12, 1, 14, 1, 17, 1, 31, 1, 5, 1, 60, 1, 38, 1, 9, 1, 47, 1, 19, 1, 5, 1, 69, 1, 68, 1, 27, 1, 8, 1, 94, 1, 5, 1, 124, 1, 107, 1, 9, 1, 122, 1, 33, 1, 5, 1, 156, 1, 8, 1, 14, 1, 155, 1, 193, 1, 5, 1, 43, 1, 192, 1, 9, 1, 212, 1, 280, 1, 5, 1, 18, 1, 255, 1, 20, 1, 278, 1, 13, 1, 5, 1, 355, 1, 12, 1, 9, 1, 8, 1, 441, 1, 5, 1, 381, 1, 380, 1, 14 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

MathWorld, Pairing Function

FORMULA

a(n) = (1/2)*(2 + ((A001511(n)+A055396(1+n))^2) - A001511(n) - 3*A055396(1+n)).

PROG

(PARI)

A001511(n) = (1+valuation(n, 2));

A055396(n) = if(n==1, 0, primepi(factor(n)[1, 1])); \\ This function from Charles R Greathouse IV, Apr 23 2015

A286254(n) = (2 + ((A001511(n)+A055396(1+n))^2) - A001511(n) - 3*A055396(1+n))/2;

for(n=1, 10000, write("b286254.txt", n, " ", A286254(n)));

(Scheme) (define (A286254 n) (* (/ 1 2) (+ (expt (+ (A001511 n) (A055396 (+ 1 n))) 2) (- (A001511 n)) (- (* 3 (A055396 (+ 1 n)))) 2)))

(Python)

from sympy import primepi, isprime, primefactors

def T(n, m): return ((n + m)**2 - n - 3*m + 2)/2

def a049084(n): return primepi(n)*(1*isprime(n))

def a055396(n): return 0 if n==1 else a049084(min(primefactors(n)))

def a001511(n): return 2 + bin(n - 1)[2:].count("1") - bin(n)[2:].count("1")

def a(n): return T(a001511(n), a055396(n + 1)) # Indranil Ghosh, May 07 2017

CROSSREFS

Cf. A000027, A001511, A055396, A253790, A286161, A286251, A286252, A286253.

Sequence in context: A062264 A276738 A094049 * A322664 A286457 A327766

Adjacent sequences:  A286251 A286252 A286253 * A286255 A286256 A286257

KEYWORD

nonn

AUTHOR

Antti Karttunen, May 07 2017

STATUS

approved

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Last modified May 18 15:01 EDT 2021. Contains 343995 sequences. (Running on oeis4.)